A101040 - OEIS

%I #16 Feb 16 2024 14:59:56

%S 0,1,1,1,1,1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,1,1,1,0,1,1,0,0,1,0,1,0,1,1,

%T 1,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,1,0,1,0,

%U 1,0,1,0,1,1,0,0,1,0,1,0,0,1,1,0,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0

%N If n has one or two prime-factors then 1 else 0.

%C a(A033942(n))=0; for n>1: a(A037143(n))=1;

%C a(A000040(n))=1; a(A001358(n))=1;

%C A101041(n) = Sum(a(k): 1<=k<=n) + 1.

%C Primes counted with multiplicity. - _Harvey P. Dale_, Feb 16 2024

%H Antti Karttunen, <a href="/A101040/b101040.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

%F a(n) = A010051(n)+A064911(n) = 0^floor(A001222(n)/3)-0^(n-1).

%F a(1) = 0; for n > 1, a(n) = A063524(A032742(A032742(n))). - _Antti Karttunen_, Nov 23 2017

%t a[n_] := If[n == 1, 0, Boole[PrimeOmega[n] <= 2]];

%t Array[a, 105] (* _Jean-François Alcover_, Dec 02 2021 *)

%o (Scheme) (define (A101040 n) (if (= 1 n) 0 (A063524 (A032742 (A032742 n))))) ;; _Antti Karttunen_, Nov 23 2017

%o (PARI) vector(105,k,bigomega(k)<=2&&k>1) \\ _Hugo Pfoertner_, Dec 02 2021

%Y Characteristic function of A037143 (without its initial term 1).

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Nov 28 2004